Question

In a 100 litres mixture containing water and milk in equal proportion, 10 litres of mixture is replaced by 10 litres of water in succession, twice. at the end, what is the ratio of milk to water?

Answer 1

the ratio of milk to water is 9:13

Answer 2

The new ratio of milk to water = 9:13

GIVEN

Total volume of mixture = 100 liters.

Volume of mixture removed = 10 liters

TO FIND

New ratio of milk to water.

SOLUTION

we can simply solve the above problem as follows.

it is given,

The total volume of the Mixture = 100 liters

Milk and water are in equal proportions,

50 liters (milk) + 50liters(water) = 100 l

10 liters of mixture is removed = 100-10 = 90 liters.

so, 5 liters(milk) + 5liters(water) was removed.

Amount of milk and water left -

45 liters (milk) + 45litres(water)

Now, 10 liters of milk are added.

The new volume of milk and water is -

The volume of milk = 55 liters

The volume of water = 45 liters.

Now, 10 liters of this mixture are removed.

when 50 liters of milk were present, the volume of milk removed = 5 liters.

when 55 liters of milk is present, the volume of milk removed = (5/50)×55 = 5.5 liters.

Amount of water removed = 10-5.5 = 4.5 liters.

the volume of milk left = 55-5.5 = 49.5 liters

the volume of water left = 45-40.5 = 40.5 liters.

NOW, 10 liters of milk is added again.

The final volume of milk = 49.5+10 = 59.5 liters

The final volume of water = 40.5

New ratio=

$\frac{final \: volume \: of \ \: water}{final \: volume \: of \: milk} = \frac{40.5}{59.5}$

$= \frac{81}{119} = \frac{9}{13}$

Hence, The ratio of milk to water is 9:13

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